Problem: The grades on a physics midterm at Loyola are normally distributed with $\mu = 80$ and $\sigma = 5.5$. Gabriela earned a $90$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{90 - {80}}{{5.5}}} $ ${ z \approx 1.82}$ The z-score is $1.82$. In other words, Gabriela's score was $1.82$ standard deviations above the mean.